This collection of papers honors the 100th anniversary of the birth of Boris Nikolaevich Delone, whose mathematical interests centered on the geometry of positive quadratic forms. After an initial paper presenting an account of Delone's life, including his scientific work, the book centers on discrete geometry and combinatorics. The book presents new methods that permit a description of the structure of some \(L\)-bodies and \(L\)-partitionings and that, in many cases, provide a definitive description. Also studied are combinatorial-topological problems arising in the statistical Ising model, the disposition of finite point sets in convex bodies of high dimension under certain conditions, and investigations of regular partitionings of spaces of constant curvature.

Readership

Combinatorialists and number theorists with interest in geometric matters.

Table of Contents

• D. K. Faddeev, N. P. Dolbilin, S. S. Ryshkov, and M. I. Shtogrin -- Boris Nikolaevich Delone (on his life and creative work)
• M. M. Anzin -- On variations of positive quadratic forms (with applications to the study of perfect forms)
• E. P. Baranovskiĭ -- Partitioning of Euclidean space into \(L\)-polytopes of some perfect lattices
• A. N. Dranishnikov -- Spanier-Whitehead duality and the stability of the intersection of compacta
• N. P. Dolbilin, M. A. Shtan'ko, and M. I. Shtogrin -- Combinatorial questions of the two-dimensional Ising model
• N. P. Dolbilin, M. A. Shtan'ko, and M. I. Shtogrin -- Quadrillages and parametrizations of lattice cycles
• O. R. Karalashvili -- On mappings of cubic manifolds into the standard lattice of Euclidean space
• M. D. Kovalev -- On the curvatures of tangent spheres
• V. S. Makarov -- On a nonregular partitioning of \(n\)-dimensional Lobachevsky space by congruent polytopes
• V. S. Makarov and K. P. Makarova -- On a geodesic on a Seifert-Weber manifold
• E. A. Morozova and N. N. Chentsov -- Projective Euclidean geometry and noncommutative probability theory
• M. M. Postnikov -- Three-dimensional spherical forms
• S. S. Ryshkov, S. A. Chepanov, and N. N. Yakovlev -- On the dissociation of point systems
• K. A. Sitnikov and E. E. Skurikhin -- Homology on presheaves of sets
• S. S. Ryshkov and R. M. Èrdal -- Dual systems of integer vectors and their application to the theory of \((0,1)\)-matrices